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me when you actually take my advice. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

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⣿⣻⣟⣯⣟⣿⣻⣿⣽⣿⣽⣯⣿⣹⣭⢯⡽⢭⣳⣽⣿⡿⣟⣫⢛⣼⠛⣌⢣⠛⣦⡳⡘⢆⣣⢣⣙⠲⣍⢛⢾⣙⢟⡿⣷⣮⣙⠭⣟⡽⣿⣿⣿⣻⣟⣿⣻⢿⣟⣿⡿⣿⣿⣿⣿ ⣿⣳⣟⡾⣽⢾⣽⣿⣿⣟⢿⡻⣟⡿⣿⣿⣿⣿⣿⣟⡹⣜⡋⢦⡹⣅⠫⡔⢣⡙⢤⠚⡳⡌⢆⠣⣌⠳⡌⣎⠖⡬⢳⣜⢎⡝⢿⣷⣌⡹⣿⣿⣿⣳⣻⢾⣽⣻⢾⣯⣿⣟⣷⣿⣾ ⣿⣳⣯⢿⣽⡻⣾⣿⣿⣞⢧⡻⣜⡳⡵⣺⣿⣟⠷⣡⠟⣤⢙⣲⠓⣌⠳⢌⠣⡜⢢⡙⡴⡙⣎⡱⢌⡱⡘⠼⣞⢌⡣⢜⠳⣜⢳⢜⢻⣿⣿⣿⣿⣳⢯⣟⡾⣽⣯⢷⣿⣾⢿⣾⣿ ⣿⣳⢯⣟⣶⣻⢽⣿⣿⣯⢷⡹⣎⢓⣾⡿⡣⢇⢳⡏⡜⡤⢃⡾⠱⣌⠚⡬⠱⣌⠣⡌⠽⣖⠸⡇⢎⠴⣉⠳⡜⣮⢜⠣⣝⡸⢳⣫⣳⡙⢿⣿⣏⢯⣟⢾⣽⣳⢯⣿⣞⣯⣿⣷⣿ ⣿⣽⣻⣞⣳⡟⣮⢿⣿⣿⣯⣳⢫⣿⡟⡯⢱⡍⣾⠜⣢⠕⣩⣇⠳⣌⠱⡌⠳⣄⠳⣌⠣⢽⡣⠽⣎⠶⣡⢏⡼⣙⣎⢷⣌⡳⢻⣹⣶⢹⢎⣻⣿⣦⢻⡯⣾⢽⣻⢾⣽⣻⣷⢿⣻ ⣿⣞⡷⣯⢷⡻⣝⡾⢿⣿⣿⣝⣿⡿⣙⣖⢧⢺⣇⡛⢤⡛⠴⣯⠱⣌⠣⡜⡱⡌⠖⣬⡙⢦⢯⡓⡯⣖⡱⢎⠶⣡⢿⢬⠇⠀⠈⣳⢻⣧⣛⣦⢻⣿⡇⢿⡞⣯⣟⣯⣟⣷⣿⣻⣿ ⣿⢾⣽⣳⢯⣻⡝⣞⠿⣿⣿⣿⣿⡳⡗⣏⣎⣿⢧⡙⢦⣍⠳⣿⡱⢎⡕⢮⡱⢭⡹⢤⡛⣜⠺⡯⠇⠀⢝⣮⢗⠋⠊⠙⠊⠷⣼⡱⢯⣿⡵⢻⠈⠉⠠⣎⠛⢷⡾⣽⢾⣻⣾⣟⣿ ⣿⣻⢾⣭⢷⡳⣽⢫⡟⣽⣿⣿⡟⣷⣏⠶⣎⣿⠲⣝⠶⣬⢛⣿⣷⡩⢞⡱⣎⢧⡝⡶⣹⠮⣝⣽⣽⣼⠣⠋⠀⣠⢴⡾⢵⣢⠤⣉⠑⠻⠿⣋⣀⡀⠀⣴⠀⣯⠿⣽⢯⣷⢿⣾⢿ ⣿⣻⢧⣟⣟⣻⡼⢧⣻⡿⣿⣿⣿⢣⡟⡿⣤⢿⡿⣸⢧⡧⠿⢻⣿⣸⣟⣣⡜⣧⢼⣣⢇⡿⣸⡜⠄⠃⢀⣤⣻⠼⠃⢀⣀⣘⡘⠧⣟⡧⣄⣀⠛⠻⢠⣿⠀⣟⣿⣻⢿⣼⣿⣻⣿ ⣿⣽⣻⢮⡽⢧⣻⡝⡶⣱⣿⣿⣯⢻⣏⡷⣭⣿⣷⠗⢃⣠⢦⣦⢤⡤⣀⣉⠉⡚⠓⠚⠻⠍⠊⣀⣴⣚⠟⠊⢁⡤⠖⠋⠀⠀⠉⠓⠠⢬⣑⠛⠽⣲⠀⠈⡁⣙⡶⣯⣟⡾⣷⣻⣿ ⣿⡞⣷⢯⣻⡝⣶⢛⣸⢧⣿⣿⡿⣹⡿⣜⡷⠋⣠⣖⡯⠛⣁⣀⠉⠉⠓⠋⠛⠹⠽⣛⡶⣲⡿⠝⠊⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⠀⠀⣳⠞⣷⢯⣟⡷⣿⣽ ⣷⣻⠽⣞⡵⠛⡄⢺⡌⡷⣿⣿⡗⣯⠿⢥⣴⡻⠓⢉⡴⠚⠁⠈⠉⠙⠛⠒⠲⠴⢤⣤⣄⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⡐⣿⠀⠀⠀⠉⢲⣿⣽⣻⢷⣻ ⠗⡏⢋⠡⣀⠣⣜⣣⢻⡘⣽⠟⠋⠀⢀⠞⠃⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢐⣿⠀⠄⠀⠀⢸⣿⣿⣿⢿⣽ ⠀⡘⠉⠁⢱⣜⣣⡾⠛⠁⠀⢀⠤⢪⣤⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⡿⡄⠂⠀⠀⢸⣿⣿⣿⣯⢙ ⠀⠀⢀⠰⠛⠜⠁⠀⢀⣤⢮⢣⠀⠈⣿⣇⢲⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⠾⠇⠀⠀⠀⣿⠰⣿⠄⡁⠀⠀⢸⣿⣿⣿⣿⣷ ⡀⠐⠀⠀⠀⠀⣠⢶⡏⣾⢯⢇⢇⢀⡸⠿⠆⠷⢄⠀⠀⠀⢠⣤⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠿⠳⠀⠀⠀⠀⠀⠀⣿⢘⣯⡇⢧⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠙⠻⠘⠛⠁⠈⠈⠁⠀⠀⣀⡠⣮⠀⠀⠀⠈⠉⠀⠉⠿⠿⠻⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢣⣤⢶⠀⠀⡀⠀⠀⠀⣿⢸⣯⠇⡇⡤⣒⢾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠐⡖⡆⠉⢿⣧⢹⡆⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠿⠝⠀⠀⠀⣿⢸⣯⠇⡇⢧⡙⢾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣠⠖⣽⣿⣿⣿⡀⠀⠱⡱⣈⠘⣿⣇⢿⡄⠀⠀⠀⢤⣴⣖⡏⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢸⠷⠀⠀⠀⣿⢪⣿⡅⡇⢧⡙⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⣰⡟⡰⢺⣿⣿⣿⣿⣷⡀⠀⢢⢧⢈⠹⣿⡎⣧⠀⠀⠀⠈⡉⡁⢀⣠⡄⠀⠀⠀⢀⡀⢀⣀⣀⣤⣤⡴⣖⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⢸⣿⡔⡃⢧⡙⣾⣿⣿⣿⡿⣽ ⠀⠀⠘⢟⡰⢱⣟⣾⣿⣿⣿⣿⣧⡤⢄⣇⣇⠂⢿⣿⡹⣇⠀⠀⠀⠛⠛⠀⠛⠁⠀⠀⢻⣯⠛⠛⠉⠛⠈⠉⣁⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⣉⣾⡇⣷⣿⣻⡽⣯⣟⡿⣿ ⠠⣀⠀⠀⠙⠻⣮⡿⢿⣿⣿⣿⣿⣿⡜⡜⡎⡎⢄⣿⣧⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠶⢇⣤⠀⠀⢤⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣱⣿⣿⣅⣿⣷⣯⢷⣻⢾⣽⣳ ⡙⡔⢫⡶⣄⠀⢸⡹⣍⢿⣿⣿⣿⣿⣷⣍⢻⡽⡔⡘⣿⡎⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢣⣾⣿⣿⣿⢯⣟⣿⣽⡿⣽⣞⣷⣻ ⠉⠚⠽⠯⠿⣝⢏⡳⣎⣿⣿⣿⣿⣿⣿⣏⣶⣳⣻⣶⣅⠢⣉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠾⢏⣼⣿⣿⣟⣿⡿⣿⣽⢾⣿⣽⣟⣿⣾⣽ ⠀⠀⢠⣴⣽⣮⣯⣵⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣦⢱⠈⠙⣷⣤⠀⠀⠀⠀⣤⢠⣤⣴⣶⡞⣯⠛⠛⢩⠉⡍⣥⣴⣤⣭⣶⣿⣿⢻⣷⢻⣾⣿⢻⣯⣿⣿⣿⣾⡟⣷⣿ ⣶⣯⣛⢶⡳⣞⡼⣣⠷⣩⢎⡗⢮⣙⡟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣮⣱⢀⡛⠷⠞⡛⢛⠛⣋⣩⣁⣦⡴⣴⠾⣶⢳⣻⢿⣿⣿⣿⣿⣿⣿⣿⣻⢾⣯⢿⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿ ⣿⣷⣯⢷⡻⣜⢧⡳⢯⡵⣋⡞⢧⡹⣜⠶⣹⢻⡟⣿⣿⣿⣻⣿⢿⣿⣷⣾⣶⣷⣞⡯⢿⡹⣏⢿⠶⣯⢷⣛⣾⡻⣭⢷⣿⣿⣿⣿⣿⣿⣳⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿ ⣿⣿⣯⣷⣻⢽⣺⣝⡳⣞⡵⣫⠷⣙⢮⡝⣖⢫⠿⣜⡯⢿⣿⣿⣿⣯⣿⡿⣿⣿⡞⣽⣛⡷⢯⣯⣟⡼⣫⡽⣎⢷⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿ ⣿⣿⣿⣿⡽⣯⢿⡾⣵⣫⢞⡵⣫⡝⣮⡝⣮⣓⠯⣿⠼⣏⣟⡿⣿⣿⣿⣿⣿⣿⣿⡷⣯⣟⣯⢷⣽⣳⣭⣟⢿⣚⣶⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣻⣿⣳⣭⡟⣾⣱⣛⢶⡹⢶⣹⣚⣯⢿⡽⣾⣽⣳⢿⢻⣿⣿⣿⣿⣿⣿⣾⣿⣞⣾⠳⢮⡟⣯⣟⡾⣽⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣻⢿⣿⡾⣽⣳⡽⣞⢯⡽⣣⡗⣧⡿⣯⣟⣷⢯⣟⣾⣹⣚⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣀⠂⠤⣁⢂⡉⠻⢿ ⣿⣿⣿⣿⣿⡷⣿⣻⣿⣿⣷⢯⡷⣯⣟⣞⡷⣽⢲⣿⣽⣻⣾⢿⣽⣾⡱⣎⢯⡽⢷⡯⢿⣿⣿⣿⣿⢀⠀⣿⣿⣿⡿⢿⠿⢟⠻⠿⣽⡿⣿⣿⣿⣿⣿⣦⣁⣄⡘⠰⡀⢦⢈⡱⢈ ⣿⣿⣿⡿⣷⣿⣟⣿⣽⣿⣿⣯⣟⣷⣻⢾⡽⣞⣿⣿⣽⡿⣽⣿⣳⣿⣱⢯⡞⣽⢫⣝⣳⢎⡿⣹⢿⣶⣿⣯⠁⠀⠀⣀⠝⠦⡀⠀⠙⣿⣽⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⡄⠣⠔⡡

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠙⠙⠉⠙⢉⡂⠏⠄⠼⣓⡂⢄⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡇ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠟⣀⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡘⢸ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠔⢁⣤⣤⣤⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⢀⣿⡿⣛⠻⣿⣦⠘⠆⠀⠀⠀⠀⠀⠀⡠⠘⠀⡜ ⠀⠀⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⡈⣿⣌⠦⢘⣼⣿⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃ ⠀⠀⠱⡘⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠋⠉⠀⠀⠀⠀⠀⠑⢌⣿⢿⡿⠟⣃⣴⡿⠂⠀⠀⢀⠀⠀⠀⢸⡜⠀ ⠀⠀⠀⠑⢄⠀⠀⠸⣿⣿⣿⡿⢿⣿⠇⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢏⢹⠋⠉⠀⢸⠁⠀⠀⠀⠀⠀⠒⠐⠋⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠤⠽⣿⣟⣁⡀⠁⠀⠀⠮⠵⠮⠵⠦⠏⠖⠀⠀⠸⣸⡄⣀⣀⣎⣀⡀⠠⠤⠀⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠉⠉⠉⠀⢀⠶⣀⠀⠀⠀⠀⡠⠞⠉⠩⢻⡍⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠀⡇⠒⠒⡏⠀⠀⠀⢠⠀⡋⣆⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣦⣤⣤⣾⣇⠀⠀⠃⠀⠀⠀⣠⠞⡖⠀⢀⠷⢣⠀⠀⠣⠀⠀⠀⠸⠀⢸⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣈⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣤⣾⣿⠃⣠⣤⠎⠀⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠘⠤⣀⣀⠀⠀⠀⢀⣀⡃⠀⢸⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⠏⠁⠀⠀⠀⠀⠀⠢⣀⣤⠤⢄⣸⣀⣀⡅⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⡂⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⢁⠀⡇⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⡇⠸⠀⢰⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢃⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡃⠀⠸⠄⡀⠈⡙⢪⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠘⡀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⢄⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠐⠊⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣏⢽⡷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⡆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡷⣞⠧⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⠀⠑⣤⠤⠤⠤⠤⠤⠼⠁⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⢋⣷⠉⡻⣻⣦⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡉⣂⡿⡕⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠑⡝⣮⠹⢧⠹⣯⡿⣦⠀⠀⠀⠀⢰⠏⠀⠀⠰⠆⠀⠀⠀⠀⠶⠀⠀⠀⠉⠙⡄⠀⠱⡀⠀⠀⠀⠀⠀⠐⣅⣖⡟⣛⣅⡃⡽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡧⠊⠉⠁⢹⡣⢇⣮⣷⣏⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡀⠀⠀⠀⢸⠀⠀⠀⠈⠦⡀⠀⣀⠵⡗⠯⣿⡿⢃⡗⢸⠅⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡛⡽⣿⠄⢀⠼⣽⡚⡆⢷⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⠓⠒⠋⠓⠚⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣽⣍⠩⡏⣷⣟⢽⡢⡃⡇⠇⡂⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣦⡨⣷⡇⡴⠉⠀⠑⣻⣿⡍⠁⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣀⡤⠤⠤⠤⠴⠊⠉⠀⠀⠦⠄⢀⣀⣾⣷⣷⡝⣗⡿⣟⣿⡉⠀⣀⣽⢊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣅⠔⠊⠀⠀⠀⠀⡄⠜⠑⠀⠀⠁⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⢋⠑⠛⠟⠿⣱⣿⡖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣠⡄⣤⣄⡶⣤⣤⣤⡠⣄⣠⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢜⠟⣻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣿⣾⣿⣾⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣶⢶⣦⣤⣤⣀⡈⠓⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣶⣄⠱⡀⠀ ⠀⠀⠀⠀⠀⢀⡎⢀⡤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⢹⠀ ⠀⠀⠀⠀⠀⢺⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢁⡇ ⠀⠀⠀⠀⠀⠸⡟⣿⣿⡿⡿⢟⣛⣛⣯⣭⣯⣯⣵⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣮⣯⣭⣻⣻⡻⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣁⠞⠀ ⠀⠀⠀⠀⠀⠀⢠⡘⢶⣾⣿⣾⣿⣿⣾⣿⣿⣾⣿⣾⣾⣾⣷⣿⣾⣷⣾⣷⣿⣽⣯⣯⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣽⡝⠟⠛⠛⢋⡩⠤⠖⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣽⠿⡻⢿⣿⣿⣿⣿⣿⡇⡴⠒⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⢿⣾⣯⡟⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣏⠒⢦⣀⣀⡀⠀⠳⡙⢷⣟⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠙⢿⣿⣿⢿⡄⠀⠀⠀⠈⠿⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣿⠛⣾⣷⣬⢣⠀⠉⠢⣙⠻⣾⣽⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣝⣤⣀⡘⣿⣾⣿⣿⣿⣶⣶⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣁⢻⣿⣿⣿⢸⡆⠀⠀⠀⠉⠒⠀⠒⠤⠴⢍⢻⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⡼⣖⣻⣿⣿⣿⣿⣿⡳⢆⡇⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⢠⣿⣿⣿⣎⡛⣆⢤⣤⠠⡆⠀⠀⠀⠀⠀⠑⢬⡛⢿⡾⣽⣻⣽⣷⣻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣹⡼⠃⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⢹⣿⣿⣿⢱⣝⢿⣎⢻⡆⢷⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⣿⣽⣿⣾⣿⣟⡾⣽⢿⣟⣯⣿⢿⣟⣯⠿⣛⣁⡧⠞⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠁⠄⡀ ⠀⠀⢠⠾⠯⣷⣘⣿⣿⣿⡇⠯⠓⣝⣯⣽⣏⠢⢀⣀⣀⣠⢤⣿⣭⣽⣿⣻⣿⣿⣿⣿⣿⣟⡿⠤⠬⢍⣋⣙⣉⠤⠞⠉⠀⠀⠀⠀⠘⡄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠱ ⠀⣠⠋⢀⢲⡼⣿⣾⣿⣿⡇⢸⠀⠀⠙⣿⣿⣿⣷⣶⣿⣿⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣍⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⢰⢧⢶⣬⣿⣿⣿⣿⣿⣿⠆⣿⠀⠀⣰⣿⣿⣿⣿⣿⢿⣛⡧⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⡝⠄⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠄⠀⠀⠀⠀ ⣿⢶⣯⣿⣿⣿⣿⣿⣿⣿⣧⡘⢄⠀⣻⣿⣿⣿⣿⣏⣶⣹⣾⣿⣞⡷⣯⡿⣟⢿⣯⣧⠙⠘⠀⠀⠀⠚⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣦⣽⣿⡿⢏⡳⣮⣷⣿⣿⣿⣯⣿⣽⣟⣮⠷⣌⠛⣿⣆⡄⠀⠀⠰⡄⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡿⢋⣽⣚⣷⣿⢟⢻⣽⣿⣿⣿⣿⣿⣿⣾⡽⣦⣛⡤⢚⣿⣦⠀⠀⣹⣷⣌⡓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢛⣿⡿⠿⣿⡿⣿⢷⡾⣡⢯⣿⣿⡿⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⢞⡵⢊⢻⣧⡀⢿⢭⡻⣷⣦⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⢀⡼⣡⣿⣿⡿⠏⠀⠀⠀⣸⣻⣿⣿⣿⣿⣿⣿⣿⡿⣝⣧⢏⡰⠀⠂⢹⣧⠘⡇⠙⣎⢿⣽⣦⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⢐⣈⣩⢷⣳⡟⣽⠁⠀⠀⣰⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣮⡳⣌⠳⣈⠤⢹⣇⢷⠀⠈⢹⠟⣯⠑⢢⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⢒⣵⣶⢿⣽⣾⣿⣿⣱⡧⢄⠀⠀⣇⢠⡙⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⢷⡻⣜⣣⢓⠎⢦⢻⡞⠀⠀⡞⢸⡇⣀⣠⣀⠀⢤⡀⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣶⣿⣿⣯⣿⣾⣿⣿⣿⣷⡒⢶⠞⠛⣯⠟⠰⢦⠙⡛⣿⡽⣻⣷⢿⡿⣽⣏⠿⣜⠢⣍⠚⡤⠂⡇⠀⠀⡇⣿⡹⣿⠫⠿⣿⣶⣳⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢋⣹⣟⣿⣿⣿⣿⣿⡿⡻⠉⠀⢷⣾⡿⠁⠀⠀⠘⠳⠧⣄⠲⠉⠉⠯⣹⠷⣞⡿⣬⢳⡌⠓⢌⠡⡟⠀⠀⠹⣽⣷⣻⡄⠀⢹⡿⣿⣄⢻⣘⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢿⠟⣿⣿⡿⣯⠛⣗⡵⠃⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠈⠀⠰⢦⡐⠈⠇⠘⠅⢋⠣⠘⠀⠀⢀⣽⠀⠀⠀⠉⠛⠋⠀⠀⠀⡇⣿⣿⣿⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣧⡾⣻⢟⠋⡏⠞⣿⠃⠀⡠⠐⠒⠒⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⣀⢠⡅⠀⠈⢓⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢨⠉⡼⡏⠱⣇⣗⡎⠁⡜⠁⠀⠉⠉⠉⠁⠐⣂⠠⠤⣄⡀⠀⠀⠀⠀⠈⠳⣌⡈⠑⠠⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⡝⠒⣷⣇⡜⣢⣟⣧⡕⠁⡞⣀⠀⣠⢦⣄⣆⢳⠲⣈⠷⣆⠌⠙⠂⣄⠀⠀⠀⠀⠁⡔⢌⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡜⠛⡿⠟⢿⢿⠟⠋⠀⡜⠀⣘⠶⣙⠾⣽⣯⡋⣷⣩⢶⣍⡛⢦⡐⠘⠳⡀⠀⠂⠀⢹⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠓⠚⠛⠉⠁⠀⠀⡼⢀⡳⢄⠺⡍⣞⠲⡼⠀⠻⣏⠓⠯⣛⡄⠒⠨⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠑⣌⡱⢊⠌⡓⠀⠀⠀⠈⢦⠀⠈⠙⢶⣀⣀⣀⣀⣀⣤⣿⡄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⢦⣟⡾⡙⢦⢊⠥⣉⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⣀⣤⠟⠟⢁⡉⠁⢈⣉⣀⡤⠤⠄⣈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣽⣷⣮⣮⣵⢧⠶⠀⠀⣸⠃⠀⠀⠀⢶⣊⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠢⢀⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣷⣿⣾⡽⢦⠶⠃⠀⠀⠀⠀⢸⡉⢀⠀⡀⢀⡁⢀⠀⠀⢂⠀⣤⡄⢂⠀⣀⡀⠠⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢢⠐⠰⢡⣈⠦⡜⢶⡉⣶⣖⣺⣽⣻⣿⣾⣵⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⢎⡗⣫⡜⣷⢻⣷⣽⣶⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢷⡾⠽⠿⠽⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀ ⡞⠁⢀⠀⠈⠉⠉⠐⠒⠲⢤⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠁⠀⠂⠀⠉⡇ ⡇⠀⡎⠉⠒⠠⢄⡀⠀⠀⠀⠀⠉⢓⣦⣀⠄⠀⠀⠀⠀⠄⣠⠴⠊⠁⠀⠀⠀⠀⢀⡠⠄⠂⠉⡇⠀⡇ ⣿⠀⢣⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠈⠈⡳⣄⠀⢀⡴⢋⠁⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⡇⢀⡇ ⢹⢠⢸⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⡀⠈⠓⠋⠀⠨⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠁⢸⠀ ⠘⡆⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⡎⠀⡞⠀ ⠀⢳⠀⠸⡄⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⢰⠁⢰⠁⠀ ⠀⠈⢧⠄⠱⡀⠀⢀⡇⠀⡠⣆⠖⠒⠂⠒⢧⠀⠀⠀⡀⠞⠋⠉⠁⠁⠉⢃⠀⢱⡀⠀⢠⠃⢠⠇⠀⠀ ⠀⠀⠈⢧⡀⡙⠤⠎⠀⠀⢠⠂⠀⠀⠀⠀⠀⢁⢀⠂⠄⠁⠀⠀⠀⠀⠀⠰⠀⠀⠣⠴⠃⣠⠏⠀⠀⠀ ⠀⠀⠀⠀⠳⣄⢠⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⢑⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠄⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⡈⢆⠀⠄⠀⠀⠀⢀⡌⠃⡀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣾⠞⠁⠀⠀⠀⠀⠀ ⣀⡀⣀⡀⢀⠀⡀⠽⡯⠘⠟⠻⠿⢷⣤⣔⢈⡡⠀⠠⢄⢁⣢⣴⡶⢿⠟⠛⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠿⢃⡸⣿⡿⣀⠸⡟⠉⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠾⠆⡅⠈⠳⢾⡶⠟⠃⡀⠰⠆⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠑⠄⠀⠀⣀⢀⠄⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢄⣀⡀⠀⠀⢀⣀⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠒⣤⣄⣀⣀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡲⣤⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠀⠀⠀⠈⠙⠻⣷⣶⡦⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠧⠤⠤⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⠟⢹⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⠀⢀⠹⠁⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⣖⣉⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣻⣿⣿⠀⢀⣿⡇⢠⣾⣿⣿⣿⠟⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⡆⢸⣿⡇⢸⣿⢹⣿⣯⣤⣿⣸⣿⣿⣿⣿⣿⣷⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠒⢻⠟⠛⢷⣿⣿⠇⢸⠀⠙⠩⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠃⠀⢶⣀⣤⣾⣿⡟⢀⣿⣿⣻⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠴⠚⠠⠤⠒⠤⣙⠻⣿⣿⣷⣾⣿⣿⣯⣳⣐⣒⣂⣹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣀⣀⣀⠀⠈⠱⡌⠻⣿⣿⣿⣿⣿⡿⣮⣿⣿⣷⣂⡘⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⣠⠴⠒⠉⠁⠀⠈⠙⠲⢤⡉⠦⡈⠻⣿⡿⠋⠀⢀⣽⡙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡳⣄⢀⣿⠷⣤⠞⠁⡴⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⢊⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠞⠀⠌⠂⠀⠀⢿⠀⡼⠁⢸⠀⠀⠀⠀⡇⢸⠹⣤⢷⡞⠀⡇⡇⠀⠀⠀⠀⠀⠀ ⢀⠜⠁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⠃⠀⢰⠀⢹⠀⠁⢸⠞⠀⢠⠏⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢸⠀⠸⢸⠀⢸⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠘⡶⠴⢸⠤⢘⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠠⣶⣿⣶⣶⢶⣶⣴⣾⣷⣴⡞⣴⣶⡀⣴⣶⣶⣶⣲⣴⣶⣿⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢿⠀⠩⡉⡍⣍⠨⢩⠈⣍⢹⠏⠡⡍⣍⠀⠈⠉⠉⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣶⣶⣾⣿⡦⠀⣾⡶⣿⣺⣗⣾⡷⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡾⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠁⠉⠁⠀⠈⠁⠈⠁⠁⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⡛⠾⣧⣄⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀I HATE DANDYS WORLD I EMILY BETTER⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⠈⣹⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀SHRIMPO SUCKS UWU IM BETTER I ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣏⠄⠀⣽⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀DECAPITET HE HEAD IS WHAT ME HOLD⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢶⣤⣤⣀⣀⡀⠉⠈⢿⣄⣰⠿⠧⠬⠿⢷⣤⣤⣀⡀⢤⣤⣤⣤⣤⣤⣴⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⡉⠉⢛⡻⠳⢾⣿⣧⣤⣄⡀⠀⠀⢙⣷⡌⠉⠓⠦⣀⠀⠀⠀⠀⠀⣰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣶⠚⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠳⣄⠀⠀⣰⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀me⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠁⠀⠀⠀⠀⠀⠀⠀⣧⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⡿⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡀⡀⠀⠀⢀⣠⣾⡋⢘⠀⠀⠀⣸⣶⣷⠶⢶⡄⠀⠀⠻⣿⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡷⠀⠀⠉⠻⢶⣴⣟⠍⠥⠉⠙⠛⠛⢲⡿⢶⡿⣷⢬⣿⡀⠀⢀⣿⠙⠳⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⣀⣤⣶⠛⢻⡋⢳⢀⣀⡀⣶⠿⠉⢙⣻⣦⠀⠀⠀⠀⢸⣇⢨⣷⣿⢠⣿⣇⠀⣀⣿⠀⠀⣀⣼⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠿⠿⢾⣏⡁⠀⠄⠘⠷⠾⢶⣶⣴⣿⠶⠿⠛⠉⠈⠀⠀⠀⠀⠈⢹⠻⣷⣯⣸⡇⢿⠀⢼⡟⡷⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡻⣦⣁⠀⠀⠀⠈⢯⡀⠀⠀⠈⠘⢷⣴⣄⣀⡀⠀⠀⣾⡆⠀⠉⠉⠀⠸⣿⡿⢁⣿⣾⡃⠁⠀⠀⠀⠀⢀⣀⣀⣤⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠛⢶⣄⡀⠀⠀⠀⠙⠷⣦⡄⠀⠀⠉⠳⢤⡀⠀⠀⠙⠻⣭⣟⣳⣾⡿⠁⠀⣀⡤⠚⠀⠼⣦⡾⠙⠀⠀⠀⠀⠀⠀⣴⢿⠋⠉⠀⢀⣾⢿⡄⠀⠀⠀⠀shrimp head⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣾⣿⣿⡿⣧⡄⠀⠀⠀⠈⠻⣶⣀⠀⠀⠀⠈⠙⠒⠤⢴⣤⠯⠭⣽⡟⠒⠋⠁⠀⠀⠀⠀⣭⠥⠈⠀⠀⠀⠀⠀⢸⡏⠈⠂⠀⠀⢸⡿⢻⠛⢻⣶⡶⢶⡿⠿⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠟⠛⠁⠙⢷⣤⡄⠀⠀⠀⠙⠻⣤⡀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⢴⠟⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⡀⠀⣤⡾⣧⣼⡆⠈⠉⠁⠈⣷⣤⡀⠈⠉⠛⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣧⡀⠄⠀⢽⡇⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠂⠀⠀⠸⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢻⡗⠀⠀⠀⠀⠀⢀⣰⡟⠀⢾⣿⡾⡏⠑⣸⣿⣁⣇⠀⠀⠘⠻⣷⢀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢿⡤⠤⠜⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣴⠿⠄⠀⠈⢿⡿⣶⣦⠤⢤⣄⣸⡇⠀⠀⠀⣠⣴⠾⠉⠀⠀⣸⣿⢷⣾⠻⠻⠿⣿⢻⣤⣀⡀⠀⣹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣆⠀⠈⠙⠳⠶⠶⠦⣶⣤⣤⣤⢀⠀⣾⡏⠛⢶⣤⡘⠀⢘⣷⡈⠙⢶⣄⣀⣀⣈⣤⣴⠾⡏⠁⠀⠀⠀⠀⣿⢻⣆⡘⠨⣾⣦⣄⡉⠉⠻⠿⢿⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⣌⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⠖⢿⡇⠀⠀⠉⠛⢷⡾⠯⡗⠀⣼⣏⠀⠉⠉⠉⠁⠀⠀⠀⠀⣠⣤⡶⡿⠘⠿⢿⣤⣴⠷⠍⠛⠓⢶⣄⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⢶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠀⠀⠀⠀⠀⣼⢇⠀⠀⠸⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣤⣤⣤⡶⡶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⣿⣶⣤⣤⣤⣿⠿⠿⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠰⢠⢈⣻⣇⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣀⣤⡾⠋⢐⣂⣀⣀⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⣶⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⢸⣿⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣵⣶⣿⣿⣩⣿⣋⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢨⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣷⣦⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⣰⣿⠡⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠉⠉⠙⠛⠛⠲⠲⣶⣦⣤⣀⠀⠀⢀⣴⣿⡛⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⠈⢳⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠙⢻⠷⢾⣃⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠿⣿⣀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠸⣧⠿⠿⣷⠾⠷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠿⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣰⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣼⠇⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⢿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⣟⡿⣿⣻⢿⣟⡿⣟⡿⣟⡿⣿⡿⠋⣩⣍⠙⠿⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⢟⣿⡿⠿⠛⠋⠉⠁⣀⣠⡤⠴⠒⠚⠉⠉⠁⠀⠀⠀⠀ ⣿⣳⢯⣟⡾⣯⢿⡽⣯⢿⡽⣯⢿⡽⣯⣟⣷⠿⢾⣽⣳⣯⣟⡾⣽⢯⡿⣽⣻⠏⢀⣼⢏⡽⣳⣄⢀⠉⠳⣿⡾⣵⣻⢮⣷⣻⡼⠾⠛⠉⠁⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢯⡿⣞⡿⣽⢯⡿⣽⢯⡿⣽⢯⣟⣳⣿⠁⣶⢦⣤⣭⣉⡙⠛⠿⢿⣾⠷⠟⢀⣾⢭⡚⣴⢣⡛⣿⡳⣄⠀⠛⢷⡿⠛⠉⢁⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀ ⣿⢯⡿⣽⣻⡽⣯⢿⡽⣯⢿⣽⣻⢾⣽⡇⠐⣿⣚⡴⢣⠯⣝⠷⣦⣄⡀⣠⣴⣾⣋⠶⣙⠦⢧⡹⣜⣷⠈⠳⣄⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⠀⠀⠀ ⣿⢯⣟⡷⣯⢿⡽⣯⢿⣽⣻⢾⣽⣻⢾⡇⠈⣿⢦⣹⡙⣞⢬⣳⣱⣮⣿⡿⠶⠿⠛⠛⠿⠾⢧⣷⣼⡾⣧⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣯⣟⣯⣿⠀⠀⠀ ⣿⣻⢾⡽⣯⢿⡽⣯⣟⡾⣽⣻⢶⣯⢿⡇⠀⣿⢲⢣⣽⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣟⣷⣻⢷⣻⣞⣿⠀⠀⠀ ⣿⡽⣯⢿⡽⣯⣟⡷⣯⣟⡷⣯⣟⣾⠿⠃⢀⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⢀⣠⣾⣿⣻⢷⣻⢾⡽⣯⢷⣻⡇⠀⠀⠀ ⣷⣻⡽⣯⣟⡷⣯⢿⣵⣯⠿⠛⠉⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⢢⡀⣀⣴⣿⣿⠿⢾⣯⡿⣽⢯⡿⣽⢯⣿⠃⠀⠀⠀ ⣯⢷⣻⢷⣫⣿⠾⠛⠉⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢈⠉⠀⠀⠄⡀⠀⠻⣏⠉⠀⠀⢀⣾⣿⣽⣯⢿⡽⣯⣟⣿⠀⠀⠀⢠ ⡿⣞⣿⣾⠛⠉⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⢠⠓⢚⠀⣮⠆⠀⠹⣄⠀⠀⠈⠉⠉⠛⢻⣾⣳⢯⣿⡏⠀⠀⠀⣸ ⡿⣽⢿⣧⡀⠴⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢠⠀⢀⣳⠖⢂⡀⠀⠹⣆⠀⠀⠀⠀⠀⣼⣿⡽⣯⣿⠁⠀⠀⢀⠇ ⣿⡽⣯⣟⡿⣷⣦⣉⡉⠛⠛⣲⡶⠶⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡀⠈⠀⠄⠃⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⢾⣿⣳⢿⣽⡇⠀⠀⠀⡜⠀ ⣷⣻⠷⣯⣟⣷⠿⠋⢁⡴⠞⠁⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢀⣿⠀⢀⡀⢀⣻⡿⣯⣿⠀⠀⠀⢠⠇⢠ ⣯⣟⣿⠷⠋⢁⣠⠞⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣄⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⠋⣿⣇⠈⣿⣿⣟⡿⣽⡏⠀⠀⠀⡼⠀⣾ ⣷⠟⠉⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡆⠀⠀⠀⠀⠀⠀⣾⠦⠟⠀⢸⠇⠸⣿⣿⣻⢾⡽⣿⠃⠀⠀⢰⠇⣸⣿ ⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣤⠀⠀⠀⠀⠀⡾⠀⣷⠀⢀⡀⠀⠀⣰⠏⠀⠀⠀⠻⠖⠚⠛⠉⠙⠛⠛⠛⠒⠒⢶⣼⢠⡿⣞ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣿⠀⠀⠀⠀⣸⣧⣶⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣀⣠⣤⣶⡖⠀⠀⠀⠀⠀⢀⣤⠾⡇⣸⡿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⣟⢹⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⡴⠋⠀⢸⠁⣿⣽⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠠⣴⣞⠉⠀⠀⢀⡏⢸⣟⣾⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡟⣿⣿⣿⣿⣿⣿⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠓⠦⣄⡼⠀⣾⣟⡾⣵ ⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠟⢿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣿⡿⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠳⡌⠿⣾⣽⣳ ⣿⣟⡿⣿⢿⣿⣻⣟⣿⣁⣀⣠⠼⡇⠀⢩⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢻⣻⣿⣿⣿⣿⣇⠀⠸⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠸⣿⣜⣧⣶⡿⠃⠀⢸⡓⠶⠤⣤⢤⡤⣤⠽⠆⠙⣾⣳ ⠛⠿⢿⣽⣻⣞⡷⣯⣟⣿⣻⣿⣾⣇⠀⠛⠛⢿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢷⡻⣿⣿⣿⠏⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⢸⡇⢲⣤⣤⣤⣠⣠⣤⡤⠴⠟⢛ ⠷⣤⣄⣈⠉⠛⠛⠿⠾⣷⣿⣞⣿⣿⠀⠀⢠⡟⢻⡟⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⣮⣷⢾⠋⠀⠀⠀⠀⣀⣀⣼⠃⠀⠀⠀⠀⣠⡴⠚⠛⠦⣄⣀⠀⠀⠀⢸⠅⢸⡿⠟⠛⠋⣉⣠⣤⣶⣾⣿ ⣷⣤⣌⣉⠛⠓⠶⠦⣤⣄⣀⣈⡉⢛⣧⠀⡾⢡⣿⣧⣤⡈⠉⠓⢲⣶⠶⠶⡶⣾⠋⠉⠀⠀⠀⠚⣡⣴⣿⢿⣽⡟⢀⣠⡴⠞⢋⣥⣴⠿⠗⠂⠀⠉⠙⢲⣤⣼⣦⣤⣾⣷⡿⣿⣟⡿⣯⣟⣾⣳ ⡿⣽⣻⣟⡿⣿⢶⣤⣄⣀⣀⠉⠉⠙⢻⣦⣿⣿⣻⣯⣹⣿⣶⣀⠈⠉⠛⠛⠻⣿⠶⡤⢤⣤⠤⡴⣤⡾⢿⢿⣿⣛⡯⣹⣧⠈⠋⠁⣀⣀⡤⠴⠖⠚⠋⢿⣿⣟⣯⣟⡷⣯⣟⡷⣯⣟⣷⣻⢾⡽ ⣿⣳⣟⡾⣽⢯⡿⣽⣻⣟⣿⣻⢿⣻⣿⢻⣿⣿⢿⣿⣿⣿⣽⣻⣷⣤⡀⠀⣰⠃⣰⣧⠀⡿⠶⣄⣸⣧⣿⠋⢉⡉⣻⣦⡿⠗⣻⡏⠉⠀⠀⠀⠀⠀⠀⣹⣿⣞⡷⣯⣟⡷⣯⣟⣷⣻⢾⡽⣯⣟ ⣿⢯⣟⣷⣻⣞⡷⣯⢿⡽⣯⣟⡾⣯⢿⣮⣿⣯⣼⣿⡿⣿⣯⡿⣽⣿⣷⣤⡏⣠⣿⣿⡀⢳⣤⣉⠛⠿⢿⡶⠾⣗⣿⢋⣡⠶⢛⡇⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡷⣯⣟⡷⣯⢿⣽⣻⣞⡷⣯⣟ ⣿⣻⣞⣷⣻⢾⡽⣯⢿⣽⣳⢯⡿⣽⣻⣞⣿⡿⠻⣷⡿⣽⣻⣿⣿⣻⣞⡿⣷⣌⠁⢸⡗⠞⣇⠉⠙⠓⠶⠙⠛⠉⠀⠀⠀⠀⣸⣃⣀⣀⠀⠀⠀⠀⠀⣿⢷⣯⣟⡷⣯⢿⣽⣻⣞⡷⣯⣟⡷⣯ ⣿⣳⣟⡾⣽⢯⡿⣽⣻⢾⡽⣯⣟⣷⣻⢾⣽⠁⢠⣿⣿⣿⣿⣿⣷⣿⣾⣿⡽⣿⣦⠀⣹⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢩⡿⠀⠀⠀⠀⠀⣿⣟⡾⣽⣻⣽⣻⣞⡷⣯⣟⡷⣯⣟⡷ ⣿⣳⢯⡿⣽⢯⣟⡷⣯⢿⣽⣳⣟⡾⣳⣿⡃⢠⣾⣿⣷⢯⣟⣿⡆⣹⣿⣳⣟⣷⣻⣷⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⢤⣀⠀⠀⠀⠐⣿⣯⣟⣷⣻⣞⡷⣯⣟⡷⣯⣟⡷⣯⣟ ⣿⡽⣯⢿⣽⣻⢾⡽⣯⣟⣾⣳⢯⣟⣷⣻⡅⠈⢿⣟⡿⣿⣾⣟⣠⣿⢷⣻⣞⡷⣯⣟⣿⡈⢩⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣈⣙⣷⠆⠀⡈⠙⠒⠦⣼⣿⣾⡽⣞⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯ ⣿⡽⣯⣟⡾⣽⢯⣟⣷⣻⢾⣽⣻⣞⡷⣯⢿⣄⠀⠻⢿⣷⣿⣿⣻⡽⣯⢷⣯⣟⡷⣯⣟⣷⡾⠲⢶⡖⠀⠀⠀⠀⠀⠀⠈⡿⢀⣀⣀⣤⣿⢿⣶⣤⣄⣀⠉⠙⠛⠿⢷⣯⣟⡷⣯⣟⡷⣯⣟⡷ ⣿⣻⢷⣯⢿⣽⣻⣞⡷⣯⣟⣾⣳⢯⡿⣽⢯⣟⡿⣶⣶⣶⣌⡙⢿⣽⣯⣟⡾⣽⣻⢷⣯⣿⠳⣄⠀⣷⠀⠀⠀⠀⠀⠀⠀⣷⠈⣿⢯⣟⣾⢻⣼⣳⢯⣟⡿⣶⣦⣄⡀⠀⠉⠙⠓⠿⢽⣷⣯⣟ ⣿⣯⣟⣾⣻⣞⡷⣯⣟⣷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣳⣟⡾⣽⢷⣆⠉⠻⣾⣽⣳⢯⣟⣾⠃⠀⠈⢧⡿⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⣿⢾⣭⣟⡾⣭⣟⡾⣽⣳⢟⣾⣻⢿⡶⣤⣀⡀⠀⠀⠉⠙ ⣿⡷⣿⣞⣷⣯⣟⣷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣟⣿⣤⡈⠻⣿⣿⣾⠃⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⠻⣾⣭⣟⣷⣫⣽⣳⣏⣿⣾⣽⣳⣿⣽⣻⣽⣷⣦⣄⣄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠉⠉⠉⠈⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠁⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⡤⠤⠤⠤⡀⠀⠡⡠⠄⠤⠤⠤⠤⠤⠤⠤⠔⠁⠁⠀⠀⠀⢀⣀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆⠀⠀⠈⠉⡽⠁⠀⠀⣀⠤⠤⠤⠤⡄⠀⠀⠀⠈⡏⠁⡋⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⢉⡤⠪⠑⡓⠖⠀⠀⡇⢸⠬⡷⡀⠀⠀⠓⡆⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠎⠧⢀⠎⡉⠐⠫⡰⠃⡛⡯⡝⣢⣀⣅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⠽⠊⠈⠁⡰⡤⠈⠀⣜⡥⡞⢰⠁⠉⠿⠗⣿⡃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠁⠀⠬⠀⠁⠒⠀⠀⡪⠁⠫⣴⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢯⡾⡙⢁⡀⡁⠔⠀⠆⠏⠀⡇⡕⠁⣀⡠⡤⠤⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⡁⡌⡍⠀⣈⠉⠀⢠⡧⡟⠘⢉⠍⠀⠀⢹⡟⠀⠀⠀⢀⠅⠀⠀⡎⠁⠀⠀⡖⡟⠉⡇⠀⠀⢰⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢾⠁⣨⠅⡂⡠⠄⣠⠞⡯⣏⣁⡤⡋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠀⠀⠀⡟⠁⠀⢀⠇⠀⡰⠉⢓⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡈⠄⢰⡣⡵⢋⠇⣍⡗⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⢠⠏⠀⡠⠂⠁⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⣀⣭⣼⢹⢈⣜⠕⣇⡀⠈⠉⠁⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢰⡇⡇⢈⡮⠁⠀⠀⠀⡧⠤⠄⢂⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⣾⠀⣧⠏⠀⡠⠤⠤⠤⣇⣀⣀⣤⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⣈⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⠋⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣯⣅⡀⠀⣠⣾⣿⡋⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣬⣿⣿⣟⣿⢋⡁⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⣿⣿⣿⢿⣿⢿⡿⠇⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⢻⣿⠟⠛⣶⡿⣿⡿⠾⠗⢶⣦⣿⡟⠋⡛⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⠐⢢⣷⣧⣤⣀⠈⢀⣹⡇⢀⣀⡼⣸⡉⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⢣⣟⣷⣻⣛⣖⣺⣿⣿⣒⣲⣬⢧⡇⣃⣄⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣿⣿⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠸⢋⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡇⠱⣾⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣤⢹⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⡼⢤⣦⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣷⣾⣿⣿⠁⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠄⢻⣿⣿⢿⢨⡿⠷⢮⠀⠚⡿⢿⡟⠉⢻⡇⠀⠀⢿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠠⣿⣿⣤⣠⣿⣳⡟⠀⣼⡇⢈⣧⠠⠠⣇⠀⠠⢸⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡠⠤⠒⠋⠉⠁⣙⣶⡟⡽⣳⢯⠏⣰⠇⠠⠙⡇⣾⠛⡇⠈⢻⡔⠋⠘⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⡍⠉⠀⠙⡄⠀⠀⠀⠀⣠⣶⣿⠟⡝⡵⣡⠃⣰⠃⠀⠀⠀⠇⢿⠀⠸⡀⠐⣇⠀⠀⢈⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⠛⠀⣿⣀⣀⢀⡷⠤⠶⠚⣻⠿⢊⣎⡾⡜⠘⡟⠰⠃⠀⠀⠀⠀⠀⢸⠀⠀⠳⠀⠸⣦⣴⠋⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⣴⡀⡍⠉⠙⠋⠀⠀⣠⠞⠁⢀⢈⡜⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠙⣷⣷⠏⠑⢢⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠺⣧⠸⣿⢷⡉⢢⡀⣀⡠⠞⠡⠤⢤⣣⠾⢹⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠘⣇⣷⡀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⢿⣷⡏⠛⣃⣀⠉⠻⣿⡶⣌⠉⠁⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠞⣀⣀⢀⣠⣿⡟⢹⢷⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠳⣄⣀⠤⢺⠷⢤⡉⠻⣷⣦⣤⣶⣶⣶⣶⣶⣶⣶⢤⣤⣀⣀⣤⣤⣭⣄⣤⣾⠟⠚⡛⢷⣿⣷⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⣑⠁⠒⠀⡼⢹⡖⡌⢉⢶⢴⡶⣔⡞⠙⠉⠙⠙⠛⠙⠏⠉⠉⣍⢉⠁⢢⠉⣰⣾⣿⣿⣿⣧⢽⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣦⣼⣄⣈⣝⣠⠏⡞⣼⣞⣙⠀⡈⠀⠂⠀⣨⡆⠸⠘⣆⡹⣦⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣽⣼⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠏⠉⠛⠛⠛⢻⡷⢸⣿⣿⣿⠿⣿⢛⢿⣿⠻⢿⣿⣿⣿⣿⠟⠋⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⢷⡄⠀⠀⣈⣽⢻⣯⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡄⠀⠀⠘⣇⠀⠈⠃⠀⠀⠀⠀⠁⠀⠀⠀⠙⠉⠀⠀⠀⠈⠉⠙⣿⣿⣷⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⣟⠉⠉⠓⠒⠒⠤⣄⡠⠤⠐⠒⠒⠲⢶⡹⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠼⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣽⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⢄⡐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡇⢸⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⣇⢸⣿⣿⣿⡇⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣿⡏⡇⢸⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡕⣯⠳⠱⣸⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣺⣏⣿⣿⠼⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⡯⠟⠉⠀⠈⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣝⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣙⣿⣫⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢗⣯⣿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣳⡷⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⣾⣯⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⡧⣟⢽⡗⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣩⡇⢫⡆⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⢳⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠑⢦⣀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠁⠈⠒⠢⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠁⠀⠀⠀⠀

⢼⣋⡿⣿⣿⠰⣃⠞⣢⡄⠊⢢⠃⢅⠐⠁⡇⢁⠔⡱⣍⠞⣥⢛⡼⣙⢮⣙⢮⡹⣱⢋⠷⣩⠳⣍⡳⣍⡳⣍⢳⡹⣜⢣⡝⢮⡱⣍⠞⣥⢫⢜⡣⢝⡢⣿⡛⡟⡻⢻⢻⡟⣍⢹⡷ ⣢⠑⢦⡑⣆⠳⢌⠣⡕⠺⡡⡀⠀⠀⠀⠀⠁⠀⢡⠘⠣⢛⡌⣳⠼⡱⢎⡞⢦⡓⢧⡫⣝⢲⡛⣬⠳⣜⡱⢎⢧⠳⣬⠳⣜⢣⠳⣌⢻⡰⡍⠶⣉⠶⡱⢿⣭⣶⣵⣮⣾⢧⣣⣾⠷ ⡥⢛⠤⡓⣌⡓⡚⢂⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⢲⡙⡮⣝⢣⢞⣣⡝⣣⠗⣭⢞⣱⢣⠟⣬⢓⡏⣎⠷⣘⡳⢬⢣⡛⣬⢣⢧⡙⢧⣙⠲⡍⡖⠲⡔⣢⢒⣌⠲⡐⢆⢣ ⡱⢋⠖⡱⢢⡱⢍⠎⡵⡩⢦⠐⠈⠀⢀⠀⠀⠀⠀⠀⠉⠖⢩⢳⡱⢮⣙⠮⣖⠭⣇⠿⣘⢮⣱⢫⢞⡥⢯⡜⣎⡳⣍⠞⣥⢳⡙⢦⣋⠶⣙⠦⣃⢏⢖⣩⢓⡱⢆⢣⡌⢣⡙⣌⠲ ⡇⢟⡸⢃⠧⡸⣘⢻⠠⢇⠃⢄⠠⡀⡤⢀⠘⠀⡀⢣⣟⢤⣃⡿⢇⣧⢛⡧⡜⢿⣘⡟⡻⡤⢇⡟⡼⣸⢇⡼⣃⢧⡜⡻⣄⢧⠻⣄⠻⣜⢣⢻⡘⡼⣘⡄⡻⢠⡛⢤⡘⢇⡸⣀⠧ ⢎⡣⢜⡡⢞⡱⡘⣬⢙⡲⢎⡱⢲⣙⢷⢸⡘⢮⡽⣄⡙⣮⠖⣭⠳⣬⠳⣎⠽⣣⠞⣜⡳⢭⣫⢜⣳⡱⣎⢳⢭⡲⣍⡳⡜⣎⠳⣍⠳⣌⢧⠳⣸⢑⠦⡓⣍⢣⡜⡡⠞⣌⠲⣡⠚ ⣣⠓⣌⠲⡡⢖⡩⢆⡣⢝⡢⣍⢇⡞⢼⣸⢯⣚⠴⣫⠞⣧⢛⣬⢓⢧⣛⡼⣙⡖⣻⢬⡓⣏⡖⣫⠖⣵⡩⡗⢮⡱⢎⡵⡹⣌⠗⣮⠹⣜⢪⡕⢣⢎⡣⢝⡰⢣⠜⣡⢋⡔⢣⢆⡙ ⡆⢏⡔⢣⢱⢊⡴⢣⡙⢆⡳⢌⠶⣘⢇⡞⢦⣍⠳⣥⢛⡴⣋⢖⡫⢞⢦⢳⣍⡞⣱⢮⣙⠶⣩⢧⡛⣦⢝⡺⢥⣛⠼⣒⢧⡙⡞⡴⢫⡜⣥⠚⡵⣊⠵⣊⡕⢣⢎⡱⢊⡜⡡⢎⠴ ⢎⡣⢜⡡⢎⠲⣌⠣⡜⢣⡜⣩⠎⡵⢪⡜⣣⢜⡹⢆⡏⢶⡩⢎⡳⢭⡚⢧⣚⠼⣣⠞⣟⡞⣱⢎⡳⢵⢪⠳⣍⣎⠳⣍⠶⡹⣜⡱⢣⠞⣔⠫⢖⣡⠳⢬⢸⠡⡎⡔⢣⠜⡑⢎⡒ ⡣⠞⡤⢓⡌⠳⣌⠳⡘⣥⠚⡴⣙⢬⠓⡼⣑⢮⡱⢫⡜⣣⢝⡣⣝⢣⡝⣣⢞⡹⢖⡻⡜⡼⢣⢏⡝⣎⡳⣋⠶⣜⡹⣌⡳⡱⢎⡵⢋⡞⢬⡙⣎⠴⣋⠖⣣⠓⡜⣌⠣⢎⡙⢢⠱ ⣴⣉⡖⢥⢊⠵⣈⠧⡱⢂⡛⡴⣉⠶⣙⢲⢩⠖⣭⠳⣜⡱⢎⡵⣊⠷⣸⡱⢎⡝⢮⡱⣝⠺⣍⡞⡜⢶⡱⣙⠞⡴⢳⣌⢳⡙⢮⢜⢣⠞⣡⠳⡌⠶⡑⢮⠰⣍⠲⣌⠳⡌⡜⣡⠣ ⣿⣟⣛⢿⡿⢗⡡⢎⡱⣉⠖⡱⢜⠲⣉⢮⢱⡚⡴⢋⠶⣙⢎⠶⣩⠞⣥⢛⡜⣎⢧⡓⢮⡝⢦⣙⢎⢧⠳⣍⢞⡱⢣⢎⢧⡙⣎⢎⡣⢞⡡⢧⡙⡜⡱⢊⠵⣈⠇⣆⠳⡘⠴⡡⢃ ⣧⣽⡏⢻⡟⠛⡟⣦⢱⡌⠚⢱⠊⣧⡍⢲⢣⡜⢱⠋⡞⢱⡎⢳⣥⠛⣴⢫⡜⡜⣦⢹⢣⡞⢱⡎⡝⡎⢳⡜⣮⢱⠋⡞⢢⡝⣴⠊⣵⠊⣵⢢⠙⣴⠉⡇⠚⣤⠋⡔⢣⠙⣦⠑⢣ ⠰⡐⢌⡒⠬⣑⠲⡌⢦⠙⣌⠣⠞⡤⣙⡒⢎⡱⣃⠯⡜⣱⢊⡗⡬⢳⡱⢎⡵⠳⣌⠳⣎⡜⣣⢞⡱⣙⢦⠳⣌⠧⣛⢬⠣⡕⢎⡱⣃⠞⣡⢎⡱⢆⡹⢌⠳⢌⢎⡱⢊⡕⢢⡙⢢ ⢣⡙⢢⠜⡱⢌⠣⡜⢢⡙⢤⢋⠼⡰⢡⢎⠣⡕⢎⡲⡙⣔⠫⡴⢩⡓⣜⠣⢞⡱⣍⠳⡜⡼⣑⠮⡱⡍⠶⣙⢬⡚⠴⢣⡹⢌⠧⣑⠎⣜⡡⢎⡔⢣⠜⣌⠳⡌⠦⣑⠣⣌⢣⡘⡡ ⢣⠜⣡⠚⢤⢋⠴⡉⢦⢙⠢⣍⠲⣡⠓⣌⠳⣌⠳⡰⣙⢤⠛⡴⢣⢹⠰⣋⠮⡱⣌⢳⢩⠖⡥⣋⠵⣊⠗⣩⠦⡍⡝⢆⡣⣍⢚⠤⣋⠴⡑⢎⡜⣡⠚⡤⢓⡌⢣⠜⡒⢤⢃⡒⢡ ⡃⡞⢠⠙⡂⢎⠒⣩⠂⣎⠱⢌⡓⢤⢋⡔⢣⢌⠣⡕⣊⢆⡛⠴⣩⠲⣙⠴⡩⡕⡜⢪⡱⢪⡱⢌⡳⢬⡙⢆⠳⣘⠬⣃⠶⡘⣌⠳⢌⠲⣉⠖⡸⢄⠫⠔⠣⡌⢃⠎⡱⢊⠔⡨⢁

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⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠂⠊⠉⠢⢀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⠠⢊⠀⠀⠁⠀⠀⠉⡇⢤⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠠⢄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡌⠂⠀⠀⠀⠀⠀⠀⠀⡂⠀⠅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢁⠁⠈⠀⠀⠀⠁⠁⠘⠠⡈⡡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡂⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠁⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢐⣃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠧⠠⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⡾⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⡸⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠂⢥⠄⡀⣄⣀⣀⣀⡤⠅⠀⢀⠤⠀⠀⠀⠀⠀⠀⠄⡀⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠈⡔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠒⢁⠄⠀⠀⠀⡀⠀⢀⠀⠁⠀⣀⠄⡃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠁⠉⠀⠂⠂⠒⠀⠉⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠄⠄⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⡀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡐⠋⠕⠄⡀⠐⠄⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠐⠂⠔⡀⠀⠈⡦⡤⡀⠅⣀⣃⡀⠅⠀⠀⡈⠀⠀⠀⠀⠁⠀⢀⠐⠐⠉⡃⡕⠽⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠠⡈⠆⣠⡆⡒⡀⡨⡐⢠⢠⢀⠀⣲⢂⢀⠄⣀⢠⠠⢔⣤⡁⣡⣪⠄⠋⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⠀⠁⠐⢀⠭⠀⠄⠓⠂⠌⠆⠁⠒⠉⠺⠅⢃⠙⠁⠁⠀⠁⢲⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠊⠸⡄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠲⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠈⠀⠁⠀⠠⠁⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⠀⠠⠀⠀⠀⠀⠂⠠⠁⠄⠈⠀⠃⠀⠈⠀⠀⠀⠠⠀⠁⠀⠀⢠⠊⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠒⠁⠀⠀⠁⠀⠂⠀⠂⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⠐⠀⠄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⠄⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠂⠉⠐⠢⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⢀⡀⠆⠂⠉⠁⠉⠁⠉⠉⠁⠁⠉⠑⠂⠢⠅⡓⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡇⠀⠀⠈⠑⢌⢆⡀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠈⢢⡀⠀⠀⠀⢱⠣⡀⠀⠀ ⠀⠀⠀⡁⠀⠀⠀⢀⠇⠀⠀⠀⠠⠐⠁⠀⠈⢧⠀⠀⠀⠀⠀⡌⠀⠀⡠⠄⡅⠤⣀⠀⢸⠀⡃⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⡴⢋⡕⠛⠓⢧⡀⠐⠀⠀⠀⠀⡐⠀⢀⠗⠋⢙⠛⢏⡆⠁⡅⠀⡅⠀⠀ ⠀⠀⡁⠀⠀⠀⢐⠀⠀⡎⡎⠃⠀⠀⠀⠀⢽⡄⢁⠀⠀⠀⠅⠘⡍⠀⠀⡜⠀⡇⠁⠔⠀⢀⠅⠀⠀ ⠀⠀⡀⠀⠀⠀⠨⠀⣨⡗⠀⠀⠀⠀⠀⠀⠀⠃⠀⡂⠀⠀⠅⢱⠃⠀⠀⡇⢀⡆⠊⠀⠀⡊⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠨⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠁⠈⠀⠀⠀⡑⠗⠤⢄⣀⡤⠃⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⢘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠨⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⢇⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⠀⢨⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢐⠀⠀⠀⠀⠀⠼⣀⠀⠀⠀⠀⣐⠅⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠐⠀⢧⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠌⠀⠘⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⡤⠔⠋⠁⠀⢀⣀⣀⣤⠏⠀⠀⠀⠀⠀ ⠄⢀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠋⠀⢨⠀⠐⠀⠀⠀⠀⠀ ⡁⠀⠉⠆⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⡗⠋⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⠇ ⠠⠀⠀⠀⠀⠙⡕⠒⠂⠒⠂⠒⠂⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⡊⠀ ⠀⠄⠀⠀⠀⠀⠙⡄⠀⠀⠀⠠⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠑⠦⠤⠤⠔⠅⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠈⠑⠒⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⡀⡀⣀⣀⠄⠃⠀⠀⠀ ⠀⠀⠀⠈⠂⣄⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠁⠀⠀⠀⡀⠀⠀⠀⠢⠭⣒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠉⠀⠀⠀⠀⢀⠀⠁⠐⠈⠀⠀⠀⠀⠈⠑⠲⣻⠴⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡗⠋⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣭⡓⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⠋⠀⠀⠀⠀⠀⠀⢠⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⢝⢆⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡾⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⡺⢦⡀⠀ ⠀⠀⣾⣿⡟⡇⠀⠀⠀⠀⠀⢀⣠⣾⡇⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡈⢳⡀ ⢀⣼⡿⣫⡞⠀⠀⠀⢀⡠⠞⠁⡀⠀⡇⢸⡀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡝⢮⡗ ⢸⣿⣾⡗⡇⠀⠀⢠⣮⠵⠶⠶⡀⠈⢹⡀⢷⠀⠀⠀⠀⢹⠶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣏⠰⣀ ⡞⠿⡹⣳⠃⠠⢰⠏⠁⠀⠀⠀⢣⠀⠀⢧⠈⢇⡀⠀⠀⡜⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⢀⣿⠋⡇⠰⠠ ⢉⠆⠡⡟⡄⢠⣿⣠⣤⣤⣽⣙⠚⠀⠀⠈⠳⡈⢣⡀⠀⣷⣲⣚⣏⣀⣤⣀⣑⣆⠀⠀⠀⠀⣾⢣⠇⢿⠀⠁ ⠸⠀⣤⣿⡅⠘⣿⣏⣿⣿⡿⠛⡿⣆⡀⠀⠀⠹⣄⠙⣴⣿⣿⠛⠋⣭⠛⢻⡙⢻⣷⡂⠀⢠⡟⢸⠀⣰⠀⠀ ⢇⣰⠟⠚⢱⡄⢸⣿⣯⠙⠏⠒⡧⠁⠀⠀⣸⣆⠀⠓⠚⣿⡏⠀⠸⠟⠀⢺⡇⣾⠙⠀⢀⡞⢁⡞⢀⠏⠀⠀ ⣰⠏⠑⠢⣤⣿⢠⣿⢿⣄⣀⣨⠃⠀⠀⠀⠀⠙⠣⡄⠀⢸⡻⣄⣀⣀⣀⣾⡽⠃⠀⢀⡾⠁⡞⠀⡼⠀⠀⠀ ⠛⢀⡴⣮⣽⣿⣿⣯⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠈⢠⡏⠀⢠⠟⠀⣼⢣⣾⣧⣶⡀⠀ ⠀⢸⡎⠉⠀⠈⠙⠛⢄⠀⠀⠀⠀⠀⢠⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡿⢀⡖⠋⠀⣸⣇⣾⣿⣯⠝⠆⠀ ⠀⠀⠣⣄⠀⠀⠀⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⡶⠋⠀⠀⣼⡯⠛⠋⠋⠙⠂⠸⡀ ⠀⠀⠀⠈⠉⠑⠒⠒⠒⠛⠒⠊⠉⠉⠐⠒⠤⠤⠀⠀⣀⡀⠀⠀⠤⢴⠏⢀⣀⠤⣞⠋⠀⠀⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠈⠓⠠⢤⣀⣀⣀⠤⠃⠀

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⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀ ⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢐⡁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠘⠒⠂⠂⠂⠠⠀⠤⠤⠖⠃⠀⠀ ⠀⠀⠀⠀⠘⠀⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠈⠂⠄⠄⠀⣀⣀⠴⠃⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠉⠉⠃⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡊⠀⢆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⣀⡤⠒⠈⡐⠁⠀⡄⠔⠃⠀⠀⡀⠀⠀⠀⠄⠖⠀⠀⠑⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠉⢀⠔⠉⠀⡠⠁⠀⠨⠀⢰⠃⠀⠀⡆⠀⠀⠈⡀⢂⠀⠀⠀⠀⠀⠀⠀⣓⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠎⠆⠀⠀⢰⠁⠀⠀⠃⠀⠘⡄⠤⠀⠈⣀⠀⠀⠑⡂⠡⠀⠀⠀⠀⠀⠀⡅⡳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⡐⠀⠐⠀⠘⣇⠀⠀⠈⢂⠀⠈⠪⡈⠁⠂⢣⣄⣠⣈⣀⠌⡂⠀⠀⠀⢨⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠀⢘⠀⠀⡠⠤⠤⢑⡂⠂⠐⠑⠆⠉⢈⠡⠤⠤⠤⣅⠢⠀⢉⠣⠀⠀⠀⠆⠀⠘⡄⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⠨⣠⠃⢠⠤⡄⠀⠀⠀⡀⠀⠀⠠⠠⠖⢆⠀⠀⠈⡕⡄⢅⠀⠀⠀⡁⠀⠀⡸⠀⠀⠀ ⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠌⢷⡀⡡⡀⣸⠀⠀⠋⠀⠀⠀⠀⠸⠤⠾⠤⠒⠉⢀⣫⠃⠀⠠⠌⠀⠀⠀⡇⠀⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠱⡀⠃⡆⠤⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⡤⠒⣒⠟⢀⠀⠀⡌⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠱⡀⠀⠑⢜⠀⠀⠣⣄⣀⠶⢹⠀⠀⢸⠔⠉⠬⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⢆⠀⠀⠉⠉⠓⡖⠒⡟⡚⢲⠉⠁⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⢸⠀⢀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡑⡀⠀⠀⠁⣄⠀⠀⢠⠃⠀⠈⠀⠀⠑⣄⠀⠀⢃⠀⠀⠀⡃⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⡚⠉⡒⢄⠀⠀⠀⡤⠖⠓⠊⠩⠍⠡⠍⠋⠁⠀⠀⠀⠀⠀⠀⢀⠉⠓⠚⢋⠉⠉⢯⠲⡄⠀⢧⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⢈⡿⣠⣄⠈⠜⡇⠀⢸⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑⢄⠈⢫⢪⡆⠀⠣⡀⠀⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⢀⠏⠀⢀⠁⢱⡖⡇⠀⢸⡀⠀⠀⠀⣠⠊⠅⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⢷⡀⠀⠉⢄⠀⠀ ⠀⠀⡇⠀⠀⠀⢠⠃⠀⠀⢨⣰⢋⠀⡃⠀⠀⡇⠀⠀⡠⠃⢨⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡃⢣⠀⠀⠀⢠⠀ ⠀⠀⡇⠀⠀⢠⠇⠀⠀⣀⠴⢱⠪⡀⡇⠀⡀⡇⠀⢰⠃⡰⠏⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠅⠀⠀⠀⠄ ⠀⠀⡇⠀⢠⠇⠀⢀⠞⠁⢸⡼⠀⠷⠀⠀⣡⠇⠀⡇⡤⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⠃⠀⠀⠀⠀⠄ ⠀⠀⡇⡰⠃⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠁⠉⢣⠀⠀⠀⠀⠀⠃⠤⠤⠤⣀⠀⠀⠀⣀⠤⣄⡀⠀⣠⠌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢧⡀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡅⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠙⠒⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠘⣳⠀⠀ ⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠓⡄⠀⠀⠀⢸⠁⣃⠀⠀⠀⠀⢸⠁⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡏⠀⠘⡆⠀⠀⢀⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀ ⠀⠀⠀⠐⢧⡀⠀⠀⠀⢀⣀⠾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠁⠀⠀⠘⣇⠀⢰⠁⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⠀⠀⠀⠀⠛⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⢢⢄⣀⣀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⡖⠒⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⡏⠀⠀⠀⠸⡀⠀⠀⢀⡞⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠘⡟⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠘⠆⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠦⠦⠶⠶⠶⠒⠒⠒⠒⠋⠉⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠷⠶⢤⣄⣀⡀⠀⠘⠛⠐⣆⠟⢦⡴⠀⠛⠃⢀⣀⣠⡼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠈⠉⠛⠛⠧⠭⠭⠬⠭⠥⠟⠛⠛⠉⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⣀⣀⡀⡀⣀⣀⣀⣀⣀⣀⢀⡀⡀⡠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠋⠉⠉⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠈⢳⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠲⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠩⣆⠀⠀⠀⢀⡟⢇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀ ⠀⠀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠙⡆⠀⢀⡝⠀⠈⢇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡐⡞⠀⠀⠀⠙⢶⡷⠁⠀⠀⠀⢣⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⣃⢄⠀⠀⠀⠀⠀⣐⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢠⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⡇⢠⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⡾⢉⠀⠀⠠⠠⠁⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⡄⠉⠘⣿⣶⣾⣶⣖⡀ ⠀⠀⠀⠀⢀⡤⣲⣿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢱⠀⢰⣿⣿⡿⠋⠉⠙ ⠀⠀⠀⣴⡯⣋⣽⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⢿⢻⠀⠀⠀⢁ ⣦⣤⣾⣿⣷⣿⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⣁⣿⡋⠀⠀⠀⣠⠞ ⠈⠿⣿⣿⣿⣽⣿⢨⠀⢰⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⠀⠁⠀⠀⡀⠈⠁⠉⠇⠀⠀⠀⠀⣩⡆⠀⠀⣠⠟⠁⠀ ⠀⢠⡙⣷⡾⡟⣧⡿⠀⢀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡂⠀⠐⠐⢈⢭⠈⡘⠀⠀⠀⢰⣟⣷⣶⠊⡅⠀⠀⠀ ⡀⠀⢀⠊⢳⣦⢸⣾⣆⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⡀⠀⠀⡀⠁⠀⠀⠅⠈⠠⠀⠀⠄⠀⠀⣾⣻⣿⠃⡼⠁⣰⠆⠀ ⠹⣄⠀⢧⠀⢻⣿⣿⣿⣦⠀⠎⠀⠁⣁⡅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⢀⡼⢱⢿⠃⡰⠁⢀⡏⠀⢀ ⠀⢻⡄⠘⣆⠀⢻⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢡⡰⠀⠀⠁⠀⠀⠀⠉⠀⠐⠁⠀⠔⠀⠁⠂⠂⠂⠂⠘⠛⢐⣿⣿⢠⠃⢀⣾⠁⠀⢈ ⡇⠀⢿⠀⢹⡆⠘⣿⣿⣿⣿⣗⡄⠀⠈⡠⠄⠒⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠐⠒⠠⠤⠠⠀⠀⠂⠐⠀⢀⣿⣿⣿⣞⡆⢻⣿⠀⠀⠏ ⣷⠀⢨⠇⢠⣧⠀⢸⣿⣿⣿⡾⠹⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠠⠀⣸⣿⣿⣿⣧⣿⠚⠻⠀⢸⠀ ⡏⠀⡸⠀⡾⠈⢧⣈⣿⣿⣿⡟⠹⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣂⣀⡇⠀ ⢱⡀⢁⡰⠁⠀⠀⢛⡛⣿⣿⣿⠘⢠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡿⠉⠉⢉⠁⠀